x*(x-8)=212.5

Solution for x*(x-8)=212.5 equation:

x(x-8)=212.5

We move all terms to the left:

x(x-8)-(212.5)=0

We add all the numbers together, and all the variables

x(x-8)-212.5=0

We multiply parentheses

x^2-8x-212.5=0

a = 1; b = -8; c = -212.5;
Δ = b2-4ac
Δ = -82-4·1·(-212.5)
Δ = 914
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-\sqrt{914}}{2*1}=\frac{8-\sqrt{914}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+\sqrt{914}}{2*1}=\frac{8+\sqrt{914}}{2}
$